Least Common Multiple (LCM) of 70 and 85
The least common multiple (LCM) of 70 and 85 is 1190.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 70 and 85?
First, calculate the GCD of 70 and 85 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 70 ÷ 85 = 0 remainder 70 |
| 2 | 85 ÷ 70 = 1 remainder 15 |
| 3 | 70 ÷ 15 = 4 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 110 | 21890 |
| 27 and 66 | 594 |
| 82 and 161 | 13202 |
| 23 and 178 | 4094 |
| 193 and 185 | 35705 |